for any two distributions \(P\)  and \(Q\)  over \(\mathcal {X}\) . Recall that if \(P\)  and \(Q\)  have densities \(\rho _p\)  and \(\rho _q\)  respectively, then the total variation distance is half of the \(L^1\)  distance, i.e., \(D_{TV}(P, Q) = \frac{1}{2} \int _{\mathcal {X}} |\rho _p(x) - \rho _q(x) |dx\) . The choice of the distance depends on the problem on hand and will give rise to different notions of robustness. One could also consider other statistical distances such as the Wasserstein distance and Renyi divergence, which can be related to total variation (see [1]}, [2]} for details).
